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Theorem bj-ax12wlem 32844
Description: A lemma used to prove a weak version of the axiom of substitution ax-12 2160. (Temporary comment: The general statement that ax12wlem 2122 proves.) (Contributed by BJ, 20-Mar-2020.)
Hypothesis
Ref Expression
bj-ax12wlem.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
bj-ax12wlem (𝜑 → (𝜓 → ∀𝑥(𝜑𝜓)))
Distinct variable group:   𝜒,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥)

Proof of Theorem bj-ax12wlem
StepHypRef Expression
1 bj-ax12wlem.1 . 2 (𝜑 → (𝜓𝜒))
2 ax-5 1952 . 2 (𝜒 → ∀𝑥𝜒)
31, 2bj-ax12i 32843 1 (𝜑 → (𝜓 → ∀𝑥(𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1594
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952
This theorem depends on definitions:  df-bi 197  df-an 385
This theorem is referenced by:  bj-ax12w  32892
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